Discrete total variation under the multinomial, Part 2: variance under the uniform null

Nikola Banić, Neven Elezović

For the counts $(X_1,\dots ,X_n)\sim \mathrm{Mult}(N;1/n,\dots ,1/n)$ of $N$ observations in $n$ ordered bins we study the variance of the discrete total variation $d=\sum_{i=1}^{n-1}…